Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 5, Problem 5.6.25P
A beam of square cross section (a = length of each side) is bent in the plane of a diagonal (see figure). By removing a small amount of material at the top and bottom corners, as shown by the shaded triangles in the figure, you can increase the section modulus and obtain a stronger beam, even though the area of the cross section is reduced.
- Determine the ratio ß defining the areas that should be removed in order to obtain the strongest cross section in bending.
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The cross-sectional dimensions of the beam shown in the figure are r = 113 mm and r;= 87 mm. Given M₂ = 16 kN-m, a = 37º,
and ß = 53º, what are the bending stresses at points Hand K?
H
To
a
Part 1
Incorrect. Find the moment of inertia for a solid circular cross-section of radius 113 mm, then subtract the moment of
inertia for a solid circular cross-section of radius 87 mm.
Find the area moment of inertia for the cross-section about the z axis.
Į₂ =
mmª
7
For the beam and cross-sectional dimensions are shown in Figure.
(a) Draw the shear force and bending moment diagrams with all details.
(b) What is the maximum shear force and maximum bending moment in the beam.
(c) Determine the moment of inertia about the z axis.
(d) Compute the maximum shear.
(e) Found the maximum compression bending stress.
100 mm
8 mm
100
6 mm
None
Chapter 5 Solutions
Mechanics of Materials (MindTap Course List)
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